Course Description:
Music has many connections to mathematics.The ancient Greeks discovered that chords with a pleasing
sound are related to simple ratios of integers.The mathematics of rhythm has also been studied for
centuries—in fact, ancient Indian writers discovered the Fibonacci
sequence in the rhythms of Sanskrit poetry.Other connections between math and music include the
equations describing the sounds of musical instruments, the mathematics behind
digital recording, the use of symmetry and group theory in composition, the
exploration of patterns by African and Indian drummers, the application of
chaos theory to modeling the behavior of melodies, and the representation of
chords by exotic geometric objects called orbifolds.Along the way, we discuss the role of creativity in
mathematics and the ways in which mathematics has inspired musicians.

Course Objectives:This course introduces a number of
mathematical topics and investigates their applications to the analysis of
music.I intend to use the medium
of musical analysis to (1) explore mathematical concepts such as Fourier series
and tilings that are not covered in other math courses, and (2) introduce topics
such as group theory and combinatorics covered in more detail in upper-level
math courses.The course is not
proofs-based.Students will
complete a semester-long project that explores one aspect of the course in
depth.

Prerequisite:Calculus II and some musical training
(Music 1511 or the equivalent).Students with exceptional performance in Calculus I (or
AP) and musical training will be admitted on a case-by-case basis.

Texts: Daniel
Levitin, This is Your Brain on Music, Dutton, 2006.David Benson, Music: a Mathematical
Offering, Cambridge University Press,
2006.This text is available free
online or for purchase at the bookstore. (Warning:the page numbers in the online version are different from
the printed one.I will refer to
the numbers in the printed book in class.)

Quizzes:There will be a 15-minute quiz given in class
every Wednesday when there is not a problem set due, giving ten quizzes.Quizzes are based on homework “drill”
problems, readings, and class notes.There are no makeup quizzes, but your lowest two grades will be dropped.

Problem sets: There
will be four problem sets, due February 6, February 29, March 28, and April 18
(all Fridays).Strict
academic honesty policies apply.

Project:Projects explore one or more aspects of the course
in depth.The final project
includes three presentations and a written paper plus supporting materials as
appropriate.Anyone who submits a
project that I judge to be of publishable quality and submits it to a journal
or competition will receive an A for the course.

Academic
Honesty:
Dishonesty includes cheating on a test, falsifying data, misrepresenting the
work of others as your own (plagiarism), and helping another student cheat or
plagiarize. At the very least, an academic honesty infraction will result in
the filing of a violation report and a grade of zero on that particular
assignment; serious or repeated infractions of the Academic Honesty policy will
result in failure of the course. For complete information about the
University’s policy on Academic Honesty, consult the Student Handbook
2007-2008.

Attendance: Class attendance is
mandatory. Although I do not have a rigid cut policy, anyone who has
missed lots of classes and is doing poorly in the course should not expect much
sympathy from me. If you do miss a class, it is your responsibility to
obtain the notes and assignments from another.(There are no makeup quizzes.)

Students with Disabilities:Policies for students
with disabilities are posted on the course web site.